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## CLEA - Rotation Rate of Mercury

How do we know that Mercury rotates once about its axis in 59 days?

## Objective

The answer is that we measure it (obviously :-). In the mid-1960s to early 1970s, astronomers used radio transmitters on Earth to transmit a radio signal to Mercury. This signal reflected from Mercury's surface, and radio satelites on Earth measured the reflected signal. Analyzing the signal, astronomers determined the rotation rate of Mercury. In 1974, the Mercury's sidereal period was measured more precisely by the spacecraft Mariner 10 as it flew by.

In this experiment, you will simulate the experiment performed by radio astronomers in the 1960s and 70s. You will use the Doppler

## Background

The radio waves (or "light") that reflect off Mercury will be Doppler shifted. Remember that light coming from an object moving toward us will be shifted to higher freqencies. We say it is "blue shifted" since blue is at the high frequency side of the visual spectrum.

Light coming from an object moving away from us will be shifted to lower frequencies. We say it is "red shifted" since red is at the low frequency side of the visual spectrum.

Though radio waves have a much longer wavelength and lower frequency than visible light, we still refer to a radio wave that is shifted to higher frequency as blue shifted and one that is shifted to lower frequency as red shifted.

How fast an object moves is measured by how much the light from the object is shifted. The direction the object is moving is determined by whether light from the object is shifted to higher (blue shifted) or lower (red shifted) frequencies.

When a radio wave reflects off of Mercury, will it be red shifted or blue shifted? The answer depends on whether Mercury is moving toward us or away from us in its orbit and whether the part of the planet the radio wave reflects from is moving toward us or away from us.

Doppler shift. This video describes why radio waves reflected from the surface of Mercury are doppler shifted and how we can use that to determine the orbital speed and rotational speed of Mercury.

## Procedure

We will use the CLEA program called Rotation Rate of Mercury. You should have already installed it.

1. Download two files: (1) the handout that describes what to do for this experiment; (2) the spreadsheet used to do the calculations. Read the handout briefly before continuing.

2. Watch the following instructional videos that show you how to use the Rotation Rate of Mercury simulation.

CLEA: Rotation Rate of Mercury -- Part 1. This video shows you how to send the radio pulse to Mercury.

CLEA: Rotation Rate of Mercury -- Part 2. This video shows you how to measure the widths of the reflected pulses from Mercury and how to measure the frequency shift of the sub-earth pulse (the part of the wave reflecting from the center of the surface, as we see it).

3. Make the measurements described in the handout and enter your data in the spreadsheet. Enter data for fleft and fright for each pulse, as described in the handout and instructional video. Also, enter the frequency shift of the sub-earth pulse. The spreadsheet will use this data to calculate the orbital period of Mercury and the orbital speed (written as "v" in the spreadsheet) of Mercury. Note that you will have some variance in your results. Thus, the spreadsheet calculates the average period of Mercury based on your results for each pulse.

How does your result compare to the precisely measured value of 55 days?